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2011 PUMaC Individual Finals A3

Source:

September 24, 2019
geometry

Problem Statement

Let ABCABC be an equilateral triangle having sides of length 1, and let PP be a point in the interior of ΔABC\Delta ABC such that ∠ABP=15∘\angle ABP = 15 ^\circ. Find, with proof, the minimum possible value of AP+BP+CPAP + BP + CP. (Comment: In fact this question is incorrect, unfortunately. A more reasonable problem: Prove that AP+BP+CP≥3AP + BP + CP \ge \sqrt{3}.)
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